Category:Successor Mapping
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This category contains results about Successor Mapping.
Definitions specific to this category can be found in Definitions/Successor Mapping.
Let $V$ be a basic universe.
The successor mapping $s$ is the mapping on $V$ defined and denoted:
- $\forall x \in V: \map s x := x \cup \set x$
where $x$ is a set in $V$.
Peano Structure
Let $\struct {P, s, 0}$ be a Peano structure.
Then the mapping $s: P \to P$ is called the successor mapping on $P$.
Successor Mapping on Natural Numbers
Let $\N$ be the set of natural numbers.
Let $s: \N \to \N$ be the mapping defined as:
- $s = \set {\tuple {x, y}: x \in \N, y = x + 1}$
Considering $\N$ defined as a Peano structure, this is seen to be an instance of a successor mapping.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Successor Mapping"
The following 10 pages are in this category, out of 10 total.
S
- Successor Mapping is Progressing
- Successor Mapping is Slowly Progressing
- Successor Mapping on Ordinals is Strictly Progressing
- Successor of Ordinal Smaller than Limit Ordinal is also Smaller
- Successor Set of Ordinal is Ordinal
- Successor Set of Ordinary Transitive Set is Ordinary
- Successor Set of Transitive Set is Transitive